Details

analyze254.0ms (5.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
6.2%	43.7%	50%	5
9.4%	28.1%	62.5%	6
12.5%	25%	62.5%	7
15.6%	15.6%	68.8%	8
16.8%	14.4%	68.8%	9
18.5%	8.8%	72.7%	10
19.2%	7.7%	73.1%	11
20.1%	4.6%	75.2%	12
20.5%	4%	75.5%	13
21%	2.4%	76.6%	14

Compiler

Compiled 21 to 20 computations (4.8% saved)

sample23.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
1.0ms	10×	body	128	nan
1.0ms	9×	body	128	invalid

Compiler

Compiled 41 to 41 computations (0% saved)

simplify222.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	1030	21
1	1030	21

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.1b

Counts

2 → 2

Compiler

Compiled 48 to 45 computations (6.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
0.3b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

rewrite52.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_1446`
23×	`*-un-lft-identity_binary64_1425`
17×	`add-cube-cbrt_binary64_1457`
12×	`times-frac_binary64_1431`
11×	`pow1_binary64_1483`
10×	`associate-l_binary64_1368` `add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
8×	`associate-*l/_binary64_1370`
7×	`associate-r_binary64_1367`
6×	`flip--_binary64_1400` `flip3--_binary64_1429`
5×	`sqrt-prod_binary64_1440`
4×	`associate-/r*_binary64_1371` `sqrt-div_binary64_1441` `add-log-exp_binary64_1461` `frac-times_binary64_1435`
3×	`flip3-+_binary64_1428` `flip-+_binary64_1399` `associate-/l*_binary64_1372` `pow-prod-down_binary64_1493`
2×	`distribute-lft-out--_binary64_1379` `unswap-sqr_binary64_1393` `prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `associate-r/_binary64_1369` `sqrt-pow1_binary64_1442` `associate-/r/_binary64_1373` `difference-of-squares_binary64_1394` `-commutative_binary64_1358`
1×	`distribute-lft-in_binary64_1376` `frac-2neg_binary64_1436` `pow1/2_binary64_1502` `clear-num_binary64_1424` `distribute-lft-out_binary64_1378` `distribute-rgt-in_binary64_1377` `div-inv_binary64_1422` `div-exp_binary64_1473` `cbrt-undiv_binary64_1456`

Counts

4 → 99

Calls

4 calls:

17.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
11.0ms	(*.f64 (-.f64 a 1/3) 9)
9.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series282.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

124.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
83.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
39.0ms	(*.f64 (-.f64 a 1/3) 9)
36.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify49.0ms (1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5372	2236

prune160.0ms (3.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	108	5	113

Merged error: 0.0b

Counts

113 → 5

Compiler

Compiled 2567 to 1993 computations (22.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.3b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
10.4b	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))

rewrite54.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_1446`
28×	`*-un-lft-identity_binary64_1425`
25×	`times-frac_binary64_1431`
24×	`add-cube-cbrt_binary64_1457`
21×	`associate-r_binary64_1367`
13×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
11×	`pow1_binary64_1483`
10×	`associate-l_binary64_1368` `associate-*l/_binary64_1370`
8×	`sqrt-prod_binary64_1440`
6×	`flip--_binary64_1400` `sqrt-div_binary64_1441` `flip3--_binary64_1429`
4×	`associate-/r*_binary64_1371` `associate-/r/_binary64_1373` `add-log-exp_binary64_1461`
3×	`unswap-sqr_binary64_1393` `prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `associate-/l*_binary64_1372` `pow-prod-down_binary64_1493`
2×	`distribute-lft-out--_binary64_1379` `sqrt-pow1_binary64_1442` `div-inv_binary64_1422` `difference-of-squares_binary64_1394` `div-exp_binary64_1473` `cbrt-undiv_binary64_1456` `*-commutative_binary64_1358` `frac-times_binary64_1435`
1×	`frac-2neg_binary64_1436` `pow1/2_binary64_1502` `clear-num_binary64_1424` `associate-*r/_binary64_1369`

Counts

4 → 111

Calls

4 calls:

22.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
9.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
8.0ms	(*.f64 (-.f64 a 1/3) 9)
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series319.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

127.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
111.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
41.0ms	(*.f64 (-.f64 a 1/3) 9)
40.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify68.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4933	2404
1	4933	2404

prune164.0ms (3.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	123	5	128

Merged error: 0b

Counts

128 → 5

Compiler

Compiled 3027 to 2244 computations (25.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 a 1/3))
0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
0.2b	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
0.2b	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))

rewrite139.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

372×	`times-frac_binary64_1431`
248×	`add-sqr-sqrt_binary64_1446`
247×	`*-un-lft-identity_binary64_1425`
223×	`sqrt-prod_binary64_1440`
191×	`add-cube-cbrt_binary64_1457`
33×	`associate-/l*_binary64_1372`
27×	`distribute-lft-out--_binary64_1379` `difference-of-squares_binary64_1394`
18×	`sqrt-div_binary64_1441`
16×	`associate-/r/_binary64_1373`
14×	`associate-/r*_binary64_1371`
13×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
12×	`flip--_binary64_1400` `flip3--_binary64_1429`
9×	`div-inv_binary64_1422`
7×	`pow1_binary64_1483`
5×	`associate-l_binary64_1368`
4×	`associate-r_binary64_1367` `div-exp_binary64_1473` `cbrt-undiv_binary64_1456` `add-log-exp_binary64_1461` `frac-times_binary64_1435`
3×	`flip3-+_binary64_1428` `flip-+_binary64_1399`
2×	`frac-2neg_binary64_1436` `clear-num_binary64_1424` `associate-r/_binary64_1369` `associate-l/_binary64_1370`
1×	`distribute-lft-in_binary64_1376` `unswap-sqr_binary64_1393` `prod-exp_binary64_1471` `pow1/2_binary64_1502` `cbrt-unprod_binary64_1455` `distribute-lft-out_binary64_1378` `sqrt-pow1_binary64_1442` `distribute-rgt-in_binary64_1377` `associate-/l/_binary64_1374` `rem-sqrt-square_binary64_1438` `*-commutative_binary64_1358` `pow-prod-down_binary64_1493`

Counts

4 → 328

Calls

4 calls:

66.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
18.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
7.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
4.0ms	(sqrt.f64 (-.f64 a 1/3))

series336.0ms (7%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
98.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
84.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
28.0ms	(sqrt.f64 (-.f64 a 1/3))

simplify145.0ms (3%)

Algorithm

1×	egg-herbie

Counts

340 → 340

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4928	9000
1	4928	9000

prune660.0ms (13.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	340	0	340
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	340	5	345

Merged error: 0b

Counts

345 → 5

Compiler

Compiled 8710 to 6561 computations (24.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 a 1/3) (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
3.8b	(.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))))

rewrite99.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`add-sqr-sqrt_binary64_1446`
103×	`times-frac_binary64_1431`
86×	`*-un-lft-identity_binary64_1425`
78×	`sqrt-prod_binary64_1440`
56×	`add-cube-cbrt_binary64_1457`
41×	`associate-l_binary64_1368`
27×	`associate-r_binary64_1367`
18×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
16×	`sqrt-div_binary64_1441`
15×	`distribute-lft-out--_binary64_1379` `difference-of-squares_binary64_1394`
12×	`pow1_binary64_1483`
11×	`associate-*l/_binary64_1370`
9×	`unswap-sqr_binary64_1393`
7×	`associate-/r*_binary64_1371`
6×	`flip--_binary64_1400` `associate-/r/_binary64_1373` `flip3--_binary64_1429`
5×	`div-exp_binary64_1473` `associate-/l*_binary64_1372` `cbrt-undiv_binary64_1456`
4×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `sqrt-pow1_binary64_1442` `add-log-exp_binary64_1461`
3×	`div-inv_binary64_1422` `pow-prod-down_binary64_1493`
2×	`pow1/2_binary64_1502` `associate-/l/_binary64_1374`
1×	`frac-2neg_binary64_1436` `clear-num_binary64_1424` `associate-r/_binary64_1369` `div-sub_binary64_1430` `-commutative_binary64_1358` `frac-times_binary64_1435`

Counts

4 → 187

Calls

4 calls:

45.0ms	(.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))))
17.0ms	(/.f64 (-.f64 a 1/3) (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series366.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))))
100.0ms	(/.f64 (-.f64 a 1/3) (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
35.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
32.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify83.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5198	5957

prune469.0ms (9.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	199	5	204

Merged error: 0b

Counts

204 → 5

Compiler

Compiled 6941 to 5544 computations (20.1% saved)

regimes28.0ms (0.6%)

Compiler: Compiled 188 to 172 computations (8.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	24
1	24	24

end0.0ms (0%)

sample789.0ms (16.4%)

Algorithm

1×

intervals

Results

472.0ms	8000×	body	128	valid
17.0ms	266×	body	128	nan
14.0ms	254×	body	128	invalid

Compiler

Compiled 129 to 118 computations (8.5% saved)

Details

analyze254.0ms (5.3%)

sample23.0ms (0.5%)

simplify222.0ms (4.6%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

rewrite52.0ms (1.1%)

series282.0ms (5.9%)

simplify49.0ms (1%)

prune160.0ms (3.3%)

localize8.0ms (0.2%)

rewrite54.0ms (1.1%)

series319.0ms (6.6%)

simplify68.0ms (1.4%)

prune164.0ms (3.4%)

localize12.0ms (0.2%)

rewrite139.0ms (2.9%)

series336.0ms (7%)

simplify145.0ms (3%)

prune660.0ms (13.7%)

localize11.0ms (0.2%)

rewrite99.0ms (2.1%)

series366.0ms (7.6%)

simplify83.0ms (1.7%)

prune469.0ms (9.8%)

regimes28.0ms (0.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample789.0ms (16.4%)

Profiling